On non-periodic groups with non-Dedekind norm of Abelian noncyclic subgroups

F.N. Liman (Makarenko Sumy State Pedagogical University)
M.G. Drushliak (Makarenko Sumy State Pedagogical University), https://orcid.org/0000-0002-9648-2248

Abstract


Non-periodic groups without free Abelian subgroups of rank 2 with non-Dedekind norm of Abelian noncyclic subgroups are studied.

Keywords


non-periodic group; normality; normalizer; norm; norm of Abelian noncyclic subgroups

References


Drushliak M.G. "On norm of Abelian noncyclic groups in non-periodic groups", Visnyk Kyiv univ. Fiz.-mat. nauky, 2009; 1: pp. 14-18. (in Ukrainian)

Liman F.N. "Groups with constraints on normalizers of different systems of subgroups", Depon. in DNTB of Ukraine 24.11.97, #577, 97. (in Ukrainian)

Liman F.N. "Non-periodic groups with some systems of normal subgroups", Algebra and Logic, 1968; 7(4): pp. 70-86. (in Russian) doi:10.1007/BF02218666

Lukashova T.D. "On norm of Abelian noncyclic subgroups of infinite locally finite $$$p$$$-groups", Visnyk Kyiv univ. Fiz.-mat. nauky, 2004; 3: pp. 35-39. (in Ukrainian)

Semko M.M. Groups with conditions of density of normality and its generalizations for some systems, Kyiv, 1998. (in Ukrainian)

Chernikov S.N. Groups with given properties of systems of subgroups, Moscow, 1980. (in Russian)

Baer R. "Der Kern, eine Charakteristische Untergruppe", Comp. Math., 1934; 1: pp. 254-283. (in German)

Beidleman J.C., Heineken H., Newell M. "Centre and norm", Bull. Austral. Math. Soc., 2004; 69(3): pp. 457-464. doi:10.1017/S0004972700036248

Schenkman E. "On the Norm of a Group", Illinois J. Math., 1960; 4(1): pp. 150-152. doi:10.1215/ijm/1255455741

Wang J., Guo X. "On the norm of finite groups", Algebra Colloquium, 2007; 14: pp. 605-612. doi:10.1142/S1005386707000557

Wos L. "On commutative prime power subgroups of the norm", Illinois J. Math., 1958; 2(2): pp. 271-284. doi:10.1215/ijm/1255381349




DOI: https://doi.org/10.15421/241113

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2011 F.N. Liman, M.G. Drushliak

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU